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The multiphase particle-in-cell method (MP-PIC) is a numerical method for modeling particle-fluid and particle-particle interactions in a computational fluid dynamics (CFD) calculation. The MP-PIC method achieves greater stability than its particle-in-cell predecessor by simultaneously treating the solid particles as computational particles and ...
They compared the Shan and Chen (SC), Carnahan-Starling (C–S), van der Waals (vdW), Redlich–Kwong (R–K), Redlich–Kwong Soave (RKS), and Peng–Robinson (P–R) EOS. Their results revealed that the SC EOS was insufficient and that C–S, P–R, R–K, and RKS EOS are all more accurate in modeling multiphase flow of a single component.
To close the Fanno flow equation, a model for this friction term is needed. Such a closure involves problem-dependent assumptions. [54] Rayleigh flow equation. Consider the flow inside a duct with constant area and either non-adiabatic walls without volumetric heat sources or adiabatic walls with volumetric heat sources. Start with the 1D-EE.
From the 1970s onwards, multiphase flow especially in the context of the oil industry has been studied extensively due to the increasing dependence of petroleum by the world economy. [10] The 1980s saw further modelling of multiphase flow by modelling flow patterns to different pipe inclinations and diameters and different pressures and flows.
Therefore, these multiphase flow phenomena including a solid e.g.~particulate and a gaseous or fluid phase resolve the particulate phase by discrete methods, while gas or liquid flow is described by continuous methods, and therefore, is labelled the combined continuum and discrete model (CCDM) as applied by Kawaguchi et al., [5] Hoomans, [6] Xu ...
Especially, it is a robust spatial discretization method for simulating multi-phase (solid-fluid-gas) interactions. In the MPM, a continuum body is described by a number of small Lagrangian elements referred to as 'material points'. These material points are surrounded by a background mesh/grid that is used to calculate terms such as the ...
This multiphase flow equation has traditionally been the starting point for the software programmer when he/she starts transforming the equation from differential equation to difference equation in order to write a program code for a reservoir simulator to be used in the petroleum industry.
Phase-field models are usually constructed in order to reproduce a given interfacial dynamics. For instance, in solidification problems the front dynamics is given by a diffusion equation for either concentration or temperature in the bulk and some boundary conditions at the interface (a local equilibrium condition and a conservation law), [14] which constitutes the sharp interface model.